# Thread: Two Consecutive Odd Prime Numbers

1. ## Two Consecutive Odd Prime Numbers

The sum of two consecutive odd prime numbers is the square of the product of the first and fourth prime numbers. What are the two odd numbers?

2. Originally Posted by magentarita
The sum of two consecutive odd prime numbers is the square of the product of the first and fourth prime numbers. What are the two odd numbers?
Let $a=2n-1$ and $b=2n+1$ be the 2 consecutive odd prime numbers.

$a+b=4n$

The first and four prime numbers are 2 and 7.
So their product is 14, their square is 196.
So $a+b=4n=196$

solve for n

3. ## I thought....

Originally Posted by Moo
Let $a=2n-1$ and $b=2n+1$ be the 2 consecutive odd prime numbers.

$a+b=4n$

The first and four prime numbers are 2 and 7.
So their product is 14, their square is 196.
So $a+b=4n=196$

solve for n
I thought the 4 consecutive odd prime numbers were x, x + 2, x + 4, x + 6 and so on. But then I saw the words PRIME NUMBERS and that changes the whole thing, right?